%0 Journal Article
%T Calibrated Submanifolds of R^7 and R^8 with Symmetries
%A Jason Lotay
%J Mathematics
%D 2006
%I arXiv
%R 10.1093/qmath/hal015
%X The principal theory of this paper comprises a technique for constructing associative, coassociative and Cayley submanifolds of Euclidean space with symmetries, using first-order ordinary differential equations. Explicit examples of U(1)-invariant associative cones in R^7 and SU(2)-invariant Cayley 4-folds in R^8 are then produced using this method. Further examples of associative 3-folds are presented, which are ruled, and other systems of differential equations defining calibrated submanifolds in R^7 and R^8 are given.
%U http://arxiv.org/abs/math/0601764v2